4 sided die, rolled twice problem

A four-sided die is rolled twice and the scores (1, 2, 3 or 4) recorded on each roll.

(a) What is the sample space for this experiment?

(b) Let X equal the larger of the two outcomes if they are different and the common value if they are the same. Write down the probability table for x.

(c) Find a formula for the probability (mass) function, (p.m.f.), f(x).

I know Part (A).

S = {(1,1),(1,2),(1,3),(1,4),(2,1),(2,2),(2,3),(2,4),( 3,1),(3,2),(3,3),(3,4),(4,1),(4,2),(4,3),(4,4)}

I'm not sure of what there asking for Part (B). Would X be everywhere there is 3 and 4 both when its different [(3,4)?] and when they are same [(3,3) & (4,4)?]?

Part (C) I'm not sure of also but I know it would be some formula including X and the denominator being 16.

Thanks

Re: 4 sided die, rolled twice problem

Quote:

Originally Posted by

**Mizen** A four-sided die is rolled twice and the scores (1, 2, 3 or 4) recorded on each roll.

(a) What is the sample space for this experiment?

(b) Let X equal the larger of the two outcomes if they are different and the common value if they are the same. Write down the probability table for x.

(c) Find a formula for the probability (mass) function, (p.m.f.), f(x).

I know Part (A).

S = {(1,1),(1,2),(1,3),(1,4),(2,1),(2,2),(2,3),(2,4),( 3,1),(3,2),(3,3),(3,4),(4,1),(4,2),(4,3),(4,4)}

I'm not sure of what there asking for Part (B). Would X be everywhere there is 3 and 4 both when its different [(3,4)?] and when they are same [(3,3) & (4,4)?]?

Part (C) I'm not sure of also but I know it would be some formula including X and the denominator being 16.

$\displaystyle X=1$ in only one way, $\displaystyle \{(1,1)\}$.

But $\displaystyle X=4$ happens in each of $\displaystyle \{(1,4),(2,4),(3,4),(4,1),(4,2),(4,3),(4,4)\}$ or seven ways.